He may not have a fixed sleeping schedule yet, but his awake intervals should be about 1 hour now during the day. He should learn the difference between day and night, so make sure everything’s bright and lively during the day, and dark and quiet at night for him to learn. During the day, put him to sleep 1 hour after waking up (to prevent overtiredness) so you’ll need to finish feeding/tummy time, etc during that time. You can also start establishing bedtime cues/routines and do it consistently before each nap and bedtime.
No you don’t need a sleeping schedule
Cherlyn